Methods of dithering analog image information are known per se, e.g., A Survey of Electronic Techniques For Pictorial Image Reproduction, 8089 IEEE Transactions Vol. Com - 29 (1981) Dec. No. 12. Generally, in these methods, an image for dithering is scanned dot by dot by suitable means and the gray level of each dot is determined. The resulting raster of gray levels is then subdivided into contiguous sub-rasters, the dimensions of which correspond to those of a dither matrix filled by an arbitrarily preselected distribution of all the gray level thresholds possible within a sub-raster. In each subraster the gray level of each raster dot is then compared with the corresponding threshold from the dither matrix. If the gray level is greater than the threshold, the associated raster dot is allocated a logic "1" while if the gray level is lower than the threshold the associated raster dot is allocated a logic "0". In this way, the analog image information is converted to a raster of two-level pixels or picture elements by means of which, for example, it is possible to control a printer to display the image, or by means of which the image information can be transmitted over transmission lines, e.g., in facsimile applications. See also, for example, U.S. Pat. No. 4,266,249; IBM Tech. Discl. Bul. Vol. 20 No. 12 (1978) and European Application No. A2 00 24902 in which gray scale values of pixels are determined by splitting the image data into high and low frequency components.
In many cases it is necessary or desirable to be able to enlarge or reduce the image whose information is present in dithered form. In the case of facsimile transmission, reduction may be desirable in order to reduce the number of bits for transmission and hence the required transmission line bandwidth. In displaying an image using the dither information it may be necessary to adapt the information to the resolution of the printer in such a way that the resulting print has a predetermined size.
Enlargement or reduction of the image by a given factor may also be required by a user. For example, a method of reducing/enlarging an image is described in U.S. Pat. No. 4,394,693 in which to reduce an image a number of rows and columns are simply omitted depending upon the required reduction factor. To attain a reduction having a factor a/b, b-a lines/columns are omitted from each group of b lines/columns of the input image in order to give the required output image. The number of lines/columns (b-a) to be omitted is distributed as uniformly as possible over the group b lines/columns.
Similarly, to enlarge an image, a number of rows and columns are added. To obtain an enlargement having a factor c/b, c-b lines/columns are added to each group of b lines/columns of the input image. Here again the number of lines/columns (c-b) to be added is distributed as uniformly as possible over the group of b lines/columns. Each of the added lines/columns has the same pixel pattern as one of the neighboring lines/columns.
While this method can give acceptable results in the case of pure black/white images, such as drawings, a number of problems arise if the method is used in connection with dithered images containing several gray levels, e.g., photographs and the like.
Moire distortion occurs due to the more or less uniform structure in which the pixels are removed from the pixel raster in the case of reduction or with the addition of lines/columns to the raster in the case of enlargement. The uniform structure with which the pixels are omitted or added interferes with the uniform structure present in the dithered photographs as a result of the dithering method.
Moire distortion does not occur in the reduction of an image in those cases in which the omission pattern is in synchronism with the dither matrix used. This situation, however, occurs only in a very restricted number of cases, e.g., when an 8.times.8 dither matrix is used and the reduction is from 4 to 3. In that case, however, there is another important disadvantage which arises because those pixels corresponding to one and the same part of the dither matrix are consistently omitted. These omitted pixels represent a number of specific gray level thresholds, and by omitting all the pixels associated with these specific gray level thresholds the number of gray levels in the reduced image is greatly reduced. In the example of an 8.times.8 dither matrix and a reduction from 4 to 3, the number of gray levels decreases from 65 to 37 or from 33 to 19, respectively, (if each threshold occurs twice in the 8.times.8 matrix).
Attempts have been made to counteract the formation of Moire patterns by omitting or adding pixels in accordance with an arbitrary scheme such that the positions where pixels are omitted or added are not longer situated in a fixed structure. This gives an improvement in the quality of the resulting reduced image, inasmuch as the Moire distortion is more or less reduced. However, the noise in the image increases visibly with such a method so that optimum results are not obtained.
More particularly, if the display means is capable of printing or displaying each pixel with high accuracy and high fineness, the image noise produced by the method becomes very perceptible. Reducing or eliminating Moire patterns by omitting or adding the pixels in accordance with an arbitrary scheme is then replaced by a sharp increase in the noise in the image without there being any real quality improvement.
Another disadvantage of the known method is the fact that it is not possible to use excessively large reduction factors because with large reduction factors a relatively large number of pixels have to be omitted, and hence a relatively large part of the information content of the image.
Accordingly, it is an object of the present invention to provide a method by which a dithered image can be reduced or enlarged while using a wide range of conversion factors, so that the information content of the original image remains unaffected or substantially unaffected. It is a further object of the invention to provide a method in which the occurrence of Moire distortion is avoided and the signal/noise ratio of the image is affected insignificantly, if at all.